On proper colourings of hypergraphs using prescribed colours
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A. P. Rozovskaya
Abstract
We consider a generalisation of the classic combinatorial problem of P. Erdős and A. Hajnal in the theory of hypergraphs to the case of prescribed colourings. We investigate the value mpr(n, r) equal to the minimum number of edges of a hypergraph in the class of n-uniform hypergraphs with prescribed chromatic number greater than r. We obtain a lower bound for this value which is better than the known results for r ≥ 3. Moreover, we give a sufficient conditions for existence of a prescribed r-colourability of an n-uniform hypergraph in terms of restrictions on the intersections of edges. As a corollary we obtain a new bound for the characteristic 
equal to the minimum number of edges of a hypergraph in the class of n-uniform simple hypergraphs (in which any two edges have at most one common vertex) with the prescribed chromatic number greater than r.
© de Gruyter 2010
Articles in the same Issue
- Calculation of limit probabilities of the distribution of permanent of a random matrix over the field GF(p)
- On the number of coincidences of two homogeneous random walks with positive increments
- Plane sections of the generalised Pascal pyramid and their interpretations
- On proper colourings of hypergraphs using prescribed colours
- On large distances between neighbouring zeros of the Riemann zeta-function
- On some algebraic and combinatorial properties of correlation-immune Boolean functions
- Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements
- A complete solution of the minimisation problem for a set of binary two-tape automata
Articles in the same Issue
- Calculation of limit probabilities of the distribution of permanent of a random matrix over the field GF(p)
- On the number of coincidences of two homogeneous random walks with positive increments
- Plane sections of the generalised Pascal pyramid and their interpretations
- On proper colourings of hypergraphs using prescribed colours
- On large distances between neighbouring zeros of the Riemann zeta-function
- On some algebraic and combinatorial properties of correlation-immune Boolean functions
- Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements
- A complete solution of the minimisation problem for a set of binary two-tape automata
